Sensitivity study of gamma‐function pseudodynamic algorithm

Abstract

The γ‐function explicit method has been developed for pseudodynamic testing since it can have favorable numerical dissipation. This numerical dissipation originates from the use of the structure‐dependent coefficient matrices in a quadrature equation. These coefficient matrices highly depend upon initial stiffness matrix, which is experimentally determined before the pseudodynamic test. Since the initial stiffness matrix determined from an experimental procedure may be different if a different displacement is imposed upon a specified degree of freedom to obtain its corresponding column, the coefficient matrices will vary accordingly. Sensitivity studies of this variation of the coefficient matrices for numerical properties and error propagation properties are conducted herein. It is revealed by both the analytical and numerical results that the performance of the γ‐function explicit pseudodynamic algorithm for both linear elastic and nonlinear systems is insensitive to the variation of the coefficient matrices in the quadrature equation, especially for a small value of the product of the natural frequency and the size of integration time step.